I am seeing both blender 2.8 and blender 2.81 in my program list. So can I uninstall blender 2.8?
You can uninstall 2.8. Every version of Blender doesn't rely on other versions.

Updating Blender is usually done exactly how you're doing it. This is because Blender doesn't automatically update. Sometimes new versions break old files or addons, so it's up to the user to update the program by downloading it. It can be useful in certain cases to have multiple versions installed, although it's rare.

The only way to automatically update that I know of is if you install through Steam, although my understanding is that Steam basically does what you did just in the background.